We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corresponding Hamilton–Jacobi–Bellman equation, compute explicitly the optimal return function and determine the optimal policy. As a consequence of these results, the way the dividend rate and business constraints affect the optimal policy is revealed. In particular, we show that under certain relationships between the constraints and the exogenous parameters of the random processes that govern the returns, some business activities might be redundant, that is, under the optimal policy they will never be used in any scenario.
Ann. Appl. Probab.
14(4):
1810-1837
(November 2004).
DOI: 10.1214/105051604000000909
Asmussen, S., Højgaard, B. and Taksar, M. (2000). Optimal risk control and dividend distribution policies. Example of excess-of-loss reinsurance. Finance Stoch. 4 299–324. Asmussen, S., Højgaard, B. and Taksar, M. (2000). Optimal risk control and dividend distribution policies. Example of excess-of-loss reinsurance. Finance Stoch. 4 299–324.
Asmussen, S. and Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance Math. Econom. 20 1–15. 1065.91529 10.1016/S0167-6687(96)00017-0 Asmussen, S. and Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance Math. Econom. 20 1–15. 1065.91529 10.1016/S0167-6687(96)00017-0
Choulli, T., Taksar, M. and Zhou, X. Y. (2003). An optimal diffusion model of a company with constraints on risk control. SIAM J. Control Optim. 41 1946–1979. 1084.91047 10.1137/S0363012900382667 Choulli, T., Taksar, M. and Zhou, X. Y. (2003). An optimal diffusion model of a company with constraints on risk control. SIAM J. Control Optim. 41 1946–1979. 1084.91047 10.1137/S0363012900382667
Fleming, W. H. and Rishel, R. W. (1975). Deterministic and Stochastic Optimal Control. Springer, New York. 0323.49001 Fleming, W. H. and Rishel, R. W. (1975). Deterministic and Stochastic Optimal Control. Springer, New York. 0323.49001
Fleming, W. H. and Soner, H. M. (1993). Controlled Markov Processes and Viscosity Solutions. Springer, New York. 0773.60070 Fleming, W. H. and Soner, H. M. (1993). Controlled Markov Processes and Viscosity Solutions. Springer, New York. 0773.60070
Højgaard, B. and Taksar, M. (1998). Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance Math. Econom. 22 41–51. Højgaard, B. and Taksar, M. (1998). Optimal proportional reinsurance policies for diffusion models with transaction costs. Insurance Math. Econom. 22 41–51.
Højgaard, B. and Taksar, M. (1999). Controlling risk exposure and dividends pay–out schemes: Insurance company example. Math. Finance 2 153–182. MR1849002 10.1111/1467-9965.00066 Højgaard, B. and Taksar, M. (1999). Controlling risk exposure and dividends pay–out schemes: Insurance company example. Math. Finance 2 153–182. MR1849002 10.1111/1467-9965.00066
Jeanblanc-Picque, M. and Shiryaev, A. N. (1995). Optimization of the flow of dividends. Russian Math. Surveys 50 257–277. 0878.90014 10.1070/RM1995v050n02ABEH002054 Jeanblanc-Picque, M. and Shiryaev, A. N. (1995). Optimization of the flow of dividends. Russian Math. Surveys 50 257–277. 0878.90014 10.1070/RM1995v050n02ABEH002054
Lions, P. -L. and Sznitman, A.-S. (1984). Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 511–537. 0598.60060 10.1002/cpa.3160370408 Lions, P. -L. and Sznitman, A.-S. (1984). Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 511–537. 0598.60060 10.1002/cpa.3160370408
Paulsen, J. and Gjessing, H. K. (1997). Optimal choice of dividend barriers for a risk process with stochastic return on investments. Insurance Math. Econom. 20 215–223. 0894.90048 10.1016/S0167-6687(97)00011-5 Paulsen, J. and Gjessing, H. K. (1997). Optimal choice of dividend barriers for a risk process with stochastic return on investments. Insurance Math. Econom. 20 215–223. 0894.90048 10.1016/S0167-6687(97)00011-5
Radner, R. and Shepp, L. (1996). Risk vs. profit potential: A model for corporate strategy. J. Econom. Dynam. Control 20 1373–1393. 1063.91524 Radner, R. and Shepp, L. (1996). Risk vs. profit potential: A model for corporate strategy. J. Econom. Dynam. Control 20 1373–1393. 1063.91524
Taksar, M. (2000). Optimal risk and dividend distribution control models for an insurance company. Math. Methods Oper. Res. 51 1–42. 0947.91043 10.1007/s001860050001 Taksar, M. (2000). Optimal risk and dividend distribution control models for an insurance company. Math. Methods Oper. Res. 51 1–42. 0947.91043 10.1007/s001860050001
Taksar, M. and Zhou, X. Y. (1998). Optimal risk and dividend control for a company with a debt liability. Insurance Math. Econom. 22 105–122. 0907.90101 10.1016/S0167-6687(98)00012-2 Taksar, M. and Zhou, X. Y. (1998). Optimal risk and dividend control for a company with a debt liability. Insurance Math. Econom. 22 105–122. 0907.90101 10.1016/S0167-6687(98)00012-2
Yong, J. and Zhou, X. Y. (1999). Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York. 0943.93002 Yong, J. and Zhou, X. Y. (1999). Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York. 0943.93002